Calculus 3 is a course that builds upon the concepts learned in Calculus 1 and 2, with a focus on multivariable functions. The main topics covered in this course include:
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Multivariable functions: In Calculus 3, we extend the idea of a function from one input variable to multiple input variables. We will study the properties of multivariable functions and how they can be represented graphically.
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Limits of multivariable functions: We will explore the idea of limits in the context of multivariable functions, and learn how to evaluate limits using different techniques.
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Differentiation of multivariable functions: We will learn how to take partial derivatives of multivariable functions, which are derivatives with respect to one input variable while holding all other input variables constant. We will also explore the gradient, which is a vector that points in the direction of maximum increase of a function.
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Integration of multivariable functions: We will study how to integrate multivariable functions over regions in space. This will involve understanding double and triple integrals, as well as using different coordinate systems such as polar coordinates.
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Fubini’s Theorem: This theorem allows us to compute double and triple integrals by iterated integration. It states that the order of integration can be switched under certain conditions.
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Polar coordinates: In the final part of the course, we will learn about polar coordinates, which are a way of representing points in the plane using a radius and angle. We will study how to express multivariable functions in polar coordinates and how to integrate over regions in polar coordinates.
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Overall, Calculus 3 is an important course for students who wish to pursue further study in mathematics or in fields that require a strong quantitative background. The concepts learned in this course have many applications in fields such as physics, engineering, and economics.